********* Eigenvalues for the 3+1 transverse lattice ********* Couplings: 0:mu^2 1:g^2 N 2:beta 3:lambda_1 4:lambda_2 5:lambda_3 6:lambda_4 7:lambda_5 8:tau_1 9:tau_2 10:kappa_S 11:kappa_A 12:mu_F 13:mu_0^2 14:mu_1^2 15:mu_2^2 16:mu_3^2 Use chi^2 fit with 40 criteria and tolerance 0.01. Overall scale from minimizing chi^2. Parity doublets (charge,multi,state) with error for difference over average. ( 1, 5,0) and ( 1, 6,0), error 0.25 (-1, 5,0) and (-1, 6,0), error 0.25 (-1, 7,0) and (-1, 4,0), error 0.25 Spectrum for P_perp a = (0,0), ( 0.25 0) using 4 states (multiplet, charge, c^2 error for each) = (15, 1, 0.25 2 2 2) (15, -1, 0.25 2 2 2) (16, -1, 0.25 2 2 2) (16, 1, 0.25 2 2 2) Spectrum for P_perp a = (0,0), ( 0.25 0.25) using 4 states (multiplet, charge, c^2 error for each) = (17, 1, 0.25 2 2 2) (17, -1, 0.25 2 2 2) (18, -1, 0.25 2 2 2) (18, 1, 0.25 2 2 2). Ordinary spectra multiplets, 4 states, (charge,multiplet) = ( 1, 3) (-1, 3) ( 1, 4) (-1, 4) ( 1, 5) (-1, 5) ( 1, 6) (-1, 6) (-1, 7) ( 1, 7) . All spectra extrapolated using (K,p) = (12/2,8) (12/2,6) (14/2,6) (18/2,6) . Winding potential using (n,K,p) = ( 2 0,16/2,6) ( 2 0,16/2,4) ( 2 0,26/2,4) ( 3 0,18/2,7) ( 3 0,18/2,5) ( 3 0,26/2,5) ( 4 0,16/2,8) ( 4 0,16/2,6) ( 4 0,26/2,6) . Roundness of winding using (n,K,p) = ( 2 2,14/2,8) ( 2 2,14/2,6) ( 2 2,22/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,26/2,2,3.5) ( 0 0,26/2,4,3.5) ( 0 0,26/2,2,3) ( 0 0,42/2,2,3.5) ( 0 0,42/2,2,4.25) ( 0 0,70/2,2,4) ( 0 0,70/2,2,4.5) , L = 3.577-2.726*m 5.058-3.856*m 7.154-5.452*m (all in G^2 N units); relative scale error=0.1. Roundness determined using (n,K,p,K_max) = ( 1 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,14/2,3,3.5) ( 1 0,14/2,5,3.5) ( 1 0,14/2,3,3) ( 1 0,24/2,3,4) ( 1 0,24/2,3,4.5) ( 1 0,36/2,3,5) ( 1 0,36/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,22/2,2,5) ( 1 1,22/2,4,5) ( 1 1,22/2,2,4.5) ( 1 1,44/2,2,5) ( 1 1,44/2,2,6) ( 1 1,70/2,2,6) ( 1 1,70/2,2,7) L=0+0*m and error 0.2; all in G^2 N units. p-extrapolation using n=( 1 0) and (K,p) = (14/2,3) (22/2,3) (46/2,3) (14/2,5) (28/2,5) (14/2,7) (16/2,7) . Result format: Fit info, # steps, chi^2, and p damping, scale G^2 N/sigma. The 17 couplings (G^2 N units); which couplings -- if any -- were fit. Winding potential and heavy souce potential fits. Roundness of winding potential, 1 values, and roundness of heavy source potential, 3 values, (G^2 N units) showing measured value and derived value for each. The rescaled spectrum for each P_perp*a and c^2 values. Finally come the states for the ordinary spectra. 2 11 125.4429455 -7.89775102 7.606344865 0 1 -0.2856087173 0.2219293202 -0.1696816044 30.73156699 -0.2142306992 8.610382684 -1.333819853 -1.985003664 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.143030 -0.196371 -0.834611 0.127414 -0.075777 0.192493 1.119765 0.843540 0.503180 0.385878 0.707213 0.698702 1.139320 0.489887 9.744151 9.779660 0.618115 19.353331 19.312436 -0.711865 23.309537 23.298649 -0.189523 24.317758 24.349984 0.560946 22.517383 22.530134 0.221958 33.154969 33.165085 0.176076 38.175837 38.167239 -0.149660 39.205863 39.206402 0.009384 15.250738 15.249937 -0.013953 22.517383 22.529234 0.206291 33.154969 33.105669 -0.858166 34.399901 34.402759 0.049737 24.317758 24.320896 0.054612 26.582236 26.583449 0.021127 33.996211 33.997204 0.017277 36.980026 37.313243 5.800289 9.744151 9.815132 0.617783 19.353331 19.273222 -0.697229 24.317758 24.383692 0.573850 26.582236 26.584457 0.019335 22.517383 22.547489 0.262023 33.154969 33.093790 -0.532475 35.093134 35.127343 0.297732 38.175837 38.222869 0.409341 15.250738 15.249011 -0.015038 22.517383 22.536387 0.165399 33.154969 33.121667 -0.289845 34.399901 34.429991 0.261881 23.309537 23.285894 -0.205774 24.317758 24.323086 0.046367 32.566334 32.592658 0.229114 33.944735 33.573705 -3.229250 9.744151 19.353331 28.466256 34.618594 44.579390 43.076841 48.628895 41.304269 40.551263 45.798385 47.408901 55.334623 15.250738 34.399901 40.941389 40.815775 23.309537 32.566334 33.944735 36.080348 39.205863 43.121465 42.526258 41.862370 26.582236 38.115544 49.707732 52.248645 35.093134 46.344746 48.521686 51.011872 22.517383 33.154969 38.175837 41.415320 24.317758 33.996211 36.980026 41.097405 2 11 90.04654404 -8.62518167 10.30358429 0.001967542671 1 -0.0003556352595 0.1526072913 -0.1948718176 39.22244724 -0.1235015237 16.8489298 -1.396162062 -1.969312831 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.151938 -0.167214 -0.097081 0.124507 -0.089834 0.219569 2.379138 1.036158 0.514127 0.485163 0.701267 0.732453 1.092385 0.656004 24.207434 24.232441 0.626384 25.540760 25.540739 -0.000519 29.573796 29.596929 0.579442 33.467461 33.455544 -0.298490 31.492622 31.509469 0.421988 51.344323 51.344465 0.003555 56.221644 56.229408 0.194490 56.952723 56.950617 -0.052732 25.540727 25.540706 -0.000510 31.492622 31.492621 -0.000043 51.344323 51.344291 -0.000808 56.067752 56.067752 0.000001 33.467461 33.467458 -0.000056 37.214535 37.214479 -0.001403 51.344329 51.344470 0.003552 55.999776 55.999823 0.001172 24.207434 24.257563 0.627822 25.540760 25.540735 -0.000317 33.467461 33.450271 -0.215285 34.368259 34.374242 0.074936 31.492622 31.521264 0.358715 51.344323 51.344582 0.003247 56.067765 56.067765 0.000001 56.221644 56.227649 0.075211 25.540727 25.540702 -0.000308 31.492622 31.497484 0.060894 51.344323 51.344268 -0.000694 56.067752 56.067752 0.000001 29.573796 29.618767 0.563217 33.467461 33.461540 -0.074147 41.817721 42.005955 2.357461 51.344329 51.344587 0.003243 24.207434 25.540760 34.368259 43.369337 63.257656 70.767880 70.883109 56.953536 62.543905 62.608945 66.130345 69.935696 25.540727 56.067752 57.321113 58.107767 29.573796 41.817721 52.753547 56.067765 56.952723 60.411158 70.449972 62.061861 37.214535 60.411139 65.384901 69.926733 56.067765 63.073746 68.650706 76.760596 31.492622 51.344323 56.221644 57.205077 33.467461 51.344329 55.999776 59.071640 2 29 79.36708766 -10.09107517 8.8697515 0.007919222016 1 0.1858439431 0.03282652011 -0.2497787082 74.73460463 -0.197475892 34.72017951 -1.356930985 -2.283675834 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.151260 -0.505209 0.329136 0.125296 -0.161258 0.358826 1.548781 0.746012 0.495189 0.393952 0.613958 0.632155 1.041457 0.523556 9.507398 9.555826 1.039570 18.924620 18.971815 1.013085 20.051847 20.017672 -0.733610 24.399605 24.409822 0.219337 27.090943 27.111606 0.443564 41.060276 41.080072 0.424939 43.802110 43.792325 -0.210045 45.442961 45.435725 -0.155323 19.934613 19.934114 -0.010712 27.090943 27.097012 0.130286 41.060276 41.101926 0.894064 42.503399 42.427441 -1.630526 24.399605 24.402286 0.057559 28.614358 28.614510 0.003271 41.871533 41.866650 -0.104822 42.624716 42.617351 -0.158115 9.507398 9.604329 1.040377 20.051847 19.985742 -0.709504 24.399605 24.432386 0.351841 27.961623 27.948228 -0.143774 27.090943 27.130406 0.423568 41.060276 41.039418 -0.223878 43.802110 43.797729 -0.047027 45.025777 45.078112 0.561726 19.934613 19.933535 -0.011568 27.090943 27.104729 0.147972 41.060276 41.143925 0.897810 42.503399 42.414558 -0.953541 18.924620 19.009717 0.913353 24.399605 24.393057 -0.070278 31.953263 32.032809 0.853769 38.819366 38.907108 0.941746 9.507398 20.051847 27.961623 33.245160 52.041716 52.876640 55.875163 47.471653 47.498444 50.559384 53.793084 59.662819 19.934613 42.503399 46.290354 47.820720 18.924620 31.953263 38.819366 42.092940 45.442961 48.947538 48.704167 45.571552 28.614358 45.476798 53.009824 57.007044 45.025777 53.405818 56.520882 62.576581 27.090943 41.060276 43.802110 46.634058 24.399605 41.871533 42.624716 45.925489 2 10 80.08569985 -9.703171222 6.356633011 0.01800590693 1 0.4603567256 0.03769360804 -0.2405940089 112.769386 0.01205535126 53.92982256 -1.429490563 -1.932714669 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.169863 -0.355078 -0.108878 0.133708 -0.125048 0.292707 1.775690 0.990212 0.543864 0.359250 0.713516 0.631708 1.063735 0.449344 12.012017 12.039268 0.470784 15.966203 16.029753 1.097894 16.176335 16.197644 0.368121 21.653985 21.604145 -0.861041 20.321559 20.331906 0.178758 31.603987 31.628190 0.418129 35.293833 35.280396 -0.232154 37.432578 37.437187 0.079623 20.321559 20.403176 1.410018 20.917357 20.848164 -1.195387 31.603987 31.598609 -0.092925 35.293833 35.244077 -0.859603 21.653985 21.663003 0.155803 24.777185 24.773371 -0.065887 34.044008 34.050862 0.118418 35.320474 35.304445 -0.276918 12.012017 12.066642 0.471845 16.176335 16.217207 0.353052 21.653985 21.568326 -0.739919 24.777185 24.767814 -0.080945 20.321559 20.341650 0.173543 31.603987 31.598272 -0.049370 35.293833 35.289664 -0.036015 36.639249 36.688458 0.425069 20.321559 20.482508 1.390284 20.917357 20.782063 -1.168669 31.603987 31.649886 0.396477 35.293833 35.175620 -1.021133 15.966203 16.079569 0.979262 21.653985 21.658962 0.042992 24.679381 24.795604 1.003937 30.721608 30.973755 2.178050 12.012017 16.176335 24.995026 27.263539 43.791562 45.252047 46.021699 40.545531 37.997333 40.887041 46.629394 50.769335 20.917357 36.924270 39.336162 46.631324 15.966203 24.679381 30.721608 32.045367 37.432578 45.290470 45.632384 37.642332 24.777185 38.926604 46.138776 50.992615 36.639249 44.333501 47.456357 48.276081 20.321559 31.603987 35.293833 41.148920 21.653985 34.044008 35.320474 37.984430 2 21 165.9667079 -9.511617143 2.045016211 0.03249196962 1 0.7019188198 0.047421379 -0.2825886398 148.0935677 0.04387922894 72.23754226 -1.304816549 -2.090869737 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.189452 -0.666824 0.228272 0.149544 -0.093524 0.239133 1.381544 0.877330 0.549857 0.286880 0.686553 0.626072 1.061730 0.284691 3.234384 3.245747 0.070443 5.288532 5.403403 0.712073 5.512683 5.521645 0.055559 7.634248 7.616964 -0.107145 6.738390 6.741475 0.019118 10.174696 10.184386 0.060065 11.882004 11.876305 -0.035326 12.840402 12.843387 0.018502 6.738390 6.992869 1.577498 7.413846 7.167412 -1.527630 10.174696 10.170255 -0.027531 11.882004 11.854316 -0.171633 7.634248 7.640253 0.037225 8.894476 8.892259 -0.013748 11.296229 11.299104 0.017825 11.975971 11.962855 -0.081306 3.234384 3.257189 0.070685 5.512683 5.530115 0.054031 7.634248 7.608104 -0.081032 8.823215 8.845103 0.067842 6.738390 6.746045 0.023724 10.174696 10.169459 -0.016233 11.882004 11.874410 -0.023537 12.157062 12.187796 0.095259 6.738390 7.074252 1.040990 7.413846 7.092698 -0.995387 10.174696 10.191608 0.052419 11.882004 11.824962 -0.176800 5.288532 5.451440 0.504927 7.634248 7.637990 0.011597 7.746510 8.645863 2.787513 9.355962 9.504287 0.459727 3.234384 5.512683 8.823215 10.458001 14.877300 15.569695 16.113281 14.518480 12.643234 14.314231 16.919349 18.256738 7.413846 12.545537 13.698848 16.638092 5.288532 7.746510 9.355962 9.641917 12.840402 15.750763 15.652731 13.983914 8.894476 13.292112 16.543872 16.121862 12.157062 14.503060 16.862880 16.292445 6.738390 10.174696 11.882004 14.378016 7.634248 11.296229 11.975971 13.015345 2 38 46.12090765 -9.311062037 6.6306534 0.0517766953 1 0.9934098387 0.1697639945 -0.3789815799 201.0167393 0.1580020601 92.20297604 -1.332631301 -1.718109626 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.204172 -1.007269 0.767449 0.166385 -0.109202 0.248902 1.170519 0.722038 0.600644 0.497227 0.796282 0.794966 1.087122 0.654534 10.906682 10.955022 1.047077 21.237639 21.279582 0.908516 21.425432 21.467715 0.915880 30.565147 30.500103 -1.408886 22.792018 22.800866 0.191643 34.551485 34.591855 0.874436 42.578020 42.553746 -0.525793 47.393065 47.408269 0.329336 22.792018 22.840864 1.058032 28.280264 28.270026 -0.221753 34.551485 34.542560 -0.193335 42.578020 42.494621 -1.806481 30.565147 30.597939 0.710302 36.247422 36.238342 -0.196680 40.272056 40.284679 0.273438 43.934814 43.900168 -0.750454 10.906682 11.003680 1.050521 21.425432 21.503330 0.843668 30.565147 30.478835 -0.934781 36.247422 36.227849 -0.211978 22.792018 22.816830 0.268718 34.551485 34.536455 -0.162778 42.578020 42.562694 -0.165984 43.823443 43.927096 1.122596 22.792018 22.849840 0.626232 28.280264 28.293000 0.137931 34.551485 34.634649 0.900689 42.578020 42.382683 -2.115560 21.237639 21.326677 0.964311 30.565147 30.587203 0.238875 33.352675 33.364136 0.124133 34.617251 34.738342 1.311452 10.906682 21.425432 36.304556 40.198524 51.956957 57.518855 59.230976 57.930299 46.860142 54.532146 66.823206 63.216952 28.280264 47.329536 51.864973 58.326142 21.237639 34.617251 33.352675 37.739643 47.393065 55.358267 56.550320 59.419282 36.247422 51.553230 54.459783 64.783827 43.823443 49.206651 59.124951 63.334508 22.792018 34.551485 42.578020 54.815796 30.565147 40.272056 43.934814 50.010566 2 10 169.2832014 -9.007286884 3.347773089 0.07642881742 1 0.8696096493 -0.07452362497 -0.2985128871 227.4732617 0.09475549413 110.9306354 -1.227714173 -1.861540498 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.255879 -0.677387 0.097259 0.172172 -0.096547 0.223716 2.222488 1.381801 0.636615 0.355723 0.798397 0.701635 1.195156 0.409200 7.141079 7.160942 0.272249 10.186513 10.282972 1.322069 10.425121 10.442805 0.242389 15.050657 15.023888 -0.366892 12.612010 12.616301 0.058814 19.928120 19.944942 0.230555 23.146322 23.136322 -0.137053 25.013157 25.020494 0.100559 12.612010 12.616056 0.055450 16.489860 16.498536 0.118913 19.928120 19.928767 0.008861 23.146322 23.127150 -0.262770 15.050657 15.062671 0.164664 17.338756 17.331941 -0.093410 22.009993 22.019019 0.123706 22.959249 22.953532 -0.078358 7.141079 7.180960 0.273302 10.425121 10.458402 0.228079 15.050657 15.012639 -0.260540 15.976552 15.954777 -0.149226 12.612010 12.621964 0.068214 19.928120 19.928702 0.003990 23.146322 23.148222 0.013019 25.954878 25.978737 0.163507 12.612010 12.617654 0.038673 16.489860 16.508479 0.127595 19.928120 19.963660 0.243553 23.146322 23.086899 -0.407223 10.186513 10.342303 1.067630 15.050657 15.059662 0.061710 15.892302 15.910679 0.125936 17.314889 18.778248 10.028388 7.141079 10.425121 15.976552 21.262446 28.065479 31.669065 31.328394 33.275378 26.220412 26.748450 34.017198 35.179830 16.489860 25.341112 28.482663 31.690196 10.186513 15.892302 17.314889 20.103212 25.013157 29.395497 32.249097 33.064898 17.338756 27.930137 30.727405 33.274499 25.954878 26.764896 33.233640 32.376137 12.612010 19.928120 23.146322 29.147843 15.050657 22.009993 22.959249 26.715697 2 10 174.8601833 -8.891278496 3.289181549 0.1072401379 1 0.9206767821 -0.09392462836 -0.3149533074 268.9255639 0.0849934482 131.1519588 -1.079338113 -1.832072945 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.301273 -0.592917 -0.161485 0.188198 -0.061844 0.147837 2.879267 1.797083 0.684919 0.394510 0.845107 0.764285 1.285708 0.476563 8.978225 8.998559 0.322385 12.127261 12.231588 1.654098 12.365479 12.383572 0.286861 17.171097 17.142293 -0.456694 13.448923 13.452686 0.059655 22.284251 22.299155 0.236307 25.568443 25.560931 -0.119111 27.475686 27.483412 0.122502 13.448923 13.443723 -0.082453 18.742882 18.759420 0.262214 22.284251 22.286028 0.028169 25.568443 25.555538 -0.204613 17.171097 17.182371 0.178741 19.489647 19.482788 -0.108756 24.437081 24.447526 0.165614 25.459710 25.456212 -0.055454 8.978225 9.019079 0.323868 12.365479 12.399203 0.267346 17.171097 17.129027 -0.333518 18.084805 18.061589 -0.184046 13.448923 13.457238 0.065920 22.284251 22.286903 0.021025 25.568443 25.572065 0.028709 29.131229 29.632684 3.975308 13.448923 13.438330 -0.083976 18.742882 18.775550 0.258977 22.284251 22.315821 0.250268 25.568443 25.524583 -0.347707 12.127261 12.294777 1.327987 17.171097 17.178611 0.059561 18.008718 18.024480 0.124950 18.227463 19.081319 6.768977 8.978225 12.365479 18.084805 21.812128 30.809628 34.234422 35.466534 37.824606 28.891519 30.883201 38.406010 39.705990 18.742882 28.093197 33.072848 34.005060 12.127261 18.008718 18.227463 22.835213 27.475686 32.007515 36.374886 36.971812 19.489647 32.764215 32.717505 35.988091 29.131229 30.481888 34.747847 38.116337 13.448923 22.284251 25.568443 32.184247 17.171097 24.437081 25.459710 30.185388 2 10 243.6011289 -8.918441683 2.110786823 0.1453085056 1 0.9198525335 -0.1024627408 -0.3297940584 312.689093 0.05222518693 153.7375274 -0.8797359199 -1.798794963 0 0 0 0 0 0 0 2 3 4 5 6 7 8 9 0.357550 -0.416978 -0.568230 0.205890 -0.035537 0.084481 3.838810 2.372394 0.742875 0.337881 0.900900 0.769804 1.398728 0.379298 7.659774 7.673241 0.162629 9.561896 9.742569 2.181699 9.899387 9.910258 0.131277 12.827513 12.977949 1.816577 9.457391 9.459484 0.025271 16.665613 16.673292 0.092730 18.749367 18.746791 -0.031110 19.924432 19.929266 0.058379 9.457391 9.453356 -0.048723 13.939019 13.948943 0.119843 16.665613 16.667007 0.016843 18.749367 18.744698 -0.056381 12.998676 13.004748 0.073322 14.488468 14.484548 -0.047336 18.060345 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